Question
For what values of $a$ and $b$ is the function
$
\begin{aligned}
& f(x)=\frac{x^2-4}{x-2} \text { for } x<2 \\
& =a x^2-b x+3 \text { for } 2 \leq x<3 \\
& =2 x-a+b \text { for } x \geq 3
\end{aligned}
$
continuous in its domain.
$
\begin{aligned}
& f(x)=\frac{x^2-4}{x-2} \text { for } x<2 \\
& =a x^2-b x+3 \text { for } 2 \leq x<3 \\
& =2 x-a+b \text { for } x \geq 3
\end{aligned}
$
continuous in its domain.